Lava: Foundations for Liquid Haskell via Translation to Rocq

Abstract

Liquid Haskell is an extension of the Glasgow Haskell compiler (GHC) that adds support for refinement types: types restricted by logical predicates. Specifications are automatically checked by an SMT solver, thus offering lightweight verification directly within the language. However, the necessarily large trusted codebase behind Liquid Haskell (from GHC to the SMT solver to the refinement typechecker itself) raises the question of trust in the verification and the necessity for a formalized semantics of Liquid Haskell linked to its implementation. Grounding Liquid Haskell in theory is complicated by the interaction between two semantic levels in the language: a computational one and a logical one (for refinement predicates). While both are well understood separately, their interaction is subtle and has only been partially described. We give a semantics to Liquid Haskell by translation to Rocq. Both the computational and logical parts are translated to the same language, with a well-understood semantics; our translation makes the discrepancy between the two semantic levels explicit. The translation is implemented in Haskell and comes with a Rocq library that includes powerful proof automation standing in for the SMT solver. Thus, on the practical level, our tool Lava serves as a certificate checker for the supported subset of Liquid Haskell.